Average Error: 61.9 → 0
Time: 31.1s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]
double f() {
        double r1590628 = 1.0;
        double r1590629 = -r1590628;
        double r1590630 = 2.0;
        double r1590631 = r1590629 / r1590630;
        double r1590632 = 3.0;
        double r1590633 = sqrt(r1590632);
        double r1590634 = r1590633 / r1590630;
        double r1590635 = /* ERROR: no complex support in C */;
        double r1590636 = r1590635 * r1590635;
        double r1590637 = r1590636 * r1590635;
        double r1590638 = r1590637 * r1590635;
        double r1590639 = -r1590630;
        double r1590640 = 0.0;
        double r1590641 = /* ERROR: no complex support in C */;
        double r1590642 = r1590641 * r1590635;
        double r1590643 = r1590642 * r1590635;
        double r1590644 = r1590643 * r1590635;
        double r1590645 = r1590638 + r1590644;
        double r1590646 = 5.0;
        double r1590647 = /* ERROR: no complex support in C */;
        double r1590648 = r1590647 * r1590635;
        double r1590649 = r1590648 * r1590635;
        double r1590650 = r1590645 + r1590649;
        double r1590651 = 4.0;
        double r1590652 = /* ERROR: no complex support in C */;
        double r1590653 = r1590652 * r1590635;
        double r1590654 = r1590650 + r1590653;
        double r1590655 = 7.0;
        double r1590656 = /* ERROR: no complex support in C */;
        double r1590657 = r1590654 + r1590656;
        double r1590658 = /* ERROR: no complex support in C */;
        return r1590658;
}
↓
double f() {
        double r1590659 = 5.0;
        double r1590660 = 3.0;
        double r1590661 = sqrt(r1590660);
        double r1590662 = 2.0;
        double r1590663 = r1590661 / r1590662;
        double r1590664 = 4.0;
        double r1590665 = r1590663 * r1590664;
        double r1590666 = /* ERROR: no complex support in C */;
        double r1590667 = 0.25;
        double r1590668 = r1590663 * r1590663;
        double r1590669 = r1590667 - r1590668;
        double r1590670 = -r1590661;
        double r1590671 = r1590670 / r1590662;
        double r1590672 = /* ERROR: no complex support in C */;
        double r1590673 = 6.0;
        double r1590674 = -2.0;
        double r1590675 = r1590674 * r1590661;
        double r1590676 = r1590675 / r1590662;
        double r1590677 = /* ERROR: no complex support in C */;
        double r1590678 = r1590677 + r1590672;
        double r1590679 = r1590672 * r1590678;
        double r1590680 = r1590666 + r1590679;
        double r1590681 = /* ERROR: no complex support in C */;
        return r1590681;
}


\Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))
↓
\Re(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(5 + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right) \cdot \left(\left(6 + \frac{\sqrt{3} \cdot -2}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right)\right)\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))